# How to Simplify Variable Expressions? (+FREE Worksheet!)

Learn the definition of variable and expression and how to simplify variable expressions.

## Step by step guide to simplifying variable expressions

• In algebra, a variable is a letter used to stand for a number. The most common letters are: $$x, y, z, a, b, c, m$$ and $$n$$.
• An algebraic expression is an expression contains integers, variables, and math operations such as addition, subtraction, multiplication, division, etc.
• In an expression, we can combine “like” terms. (values with the same variable and same power)

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### Simplifying Variable Expressions – Example 1:

Simplify this expression. $$2x + \ 3x + \ 4=$$$$?$$

Solution:

Combine “like” terms. Then: $$2 x \ + \ 3 x \ = 5x$$ (remember you cannot combine variables and numbers).

Then: $$2x + 3 x + \ 4=5x + \ 4$$ (remember you cannot combine variables and numbers).

### Simplifying Variable Expressions – Example 2:

Simplify this expression. $$12 \ – \ 3x^{2} \ + 5 x + \ 4 x^{2}=$$$$?$$

Solution:

Combine “like” terms: $$- \ 3x^{2} \ + 4 x^{2}=x^{2}$$
Then: $$12 \ – \ 3 x^{2} \ + \ 5x + 4 x^{2}$$ $$=12 \ + x^2 + 5x$$. Write in standard form (biggest powers first): $$x^2 \ + 5 x + \ 12$$

### Simplifying Variable Expressions – Example 3:

Simplify this expression. $$(10x+2x+3)=$$$$?$$

Solution:

Combine “like” terms: $$(10x+2x)=12x$$

Then: $$(10x+2x+3)=12x+3$$ (remember you cannot combine variables and numbers).

### Simplifying Variable Expressions – Example 4:

Simplify this expression. $$12-3x^2+9x+5x^2=$$$$?$$

Solution:

Combine “like” terms: $$-3x^2+5x^2=2x^2$$
Then: $$12-3x^2+9x+5x^2=12+2x^2+9x$$. Write in standard form (biggest powers first): $$2x^2+9x+12$$

## Exercises for Simplifying Variable Expressions

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### Simplify each expression.

• $$\color{blue}{– 2 – x^2 – 6x^2}$$
• $$\color{blue}{ 3 + 10x^2 + 2}$$
• $$\color{blue}{ 8x^2 + 6x + 7x^2}$$
• $$\color{blue}{5x^2 – 12x^2 + 8x }$$
• $$\color{blue}{– 2(4 – 6x) – 3x }$$
• $$\color{blue}{ 9 – 2x + 5x + 2}$$

• $$\color{blue}{– 7x^2 – 2}$$
• $$\color{blue}{10x^2 + 5}$$
• $$\color{blue}{15x^2 + 6x}$$
• $$\color{blue}{– 7x^2 + 8x}$$
• $$\color{blue}{9x \ – 8 }$$
• $$\color{blue}{3x \ + 11}$$

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